Is it possible to use proportional editing without affecting or hiding nearby vertices
One possible solution that is relatively cumbersome:


Add a base shape key ("Basis"), then a modification shape key ("Key 1"). 
Switch to edit mode.
Select the area that you do want to modify and assign it to a new vertex group (Group). 
Modify the mesh using proportional editing (accepting that the parts that should stay unaffected are modified for now). 
Switch back to object mode.
Set the shape key to 1 and select your vertex group ("Group") under "Blend:" to mix in the "Basis" key for the parts that should stay unaffected.
Then follow the procedure outlined in How to apply shape keys? to apply the changes to the mesh.


There are easier ways to do something like this, with major limitations:


Select the area that you don't want to affect and press Y to split it apart. Then set the proportional editing mode to "connected", thereby excluding those vertices that were previously split from the other part of the mesh. Afterwards, join the displaced seam by hand.
Limitations:
You can only do this if the area that you do want to affect is connected and in one piece.
Re-joining the seam can be cumbersome, although the remove doubles tool helps with areas that weren't modified.
Turn the part that you don't want to affect into a separate object (P with selection). If necessary, enable Object > Display > Wire for this object. Then return to the first object and edit it freely. Afterwards, re-join the meshes with Ctrl + J. Join the displaced seam by hand.
Limitations:
As before, re-joining the seam can be cumbersome.